Geodesic
Pro–p groups and towers of rational homology spheres
Boston, Nigel1 ; Ellenberg, Jordan S1
1 Department of Mathematics, University of Wisconsin, Van Vleck Hall, 480 Lincoln Drive, Madison WI 53706, USA
Geometry & topology, Tome 10 (2006) no. 1, pp. 331-334 Cet article a éte moissonné depuis la source Mathematical Sciences Publishers

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In the preceding paper, Calegari and Dunfield exhibit a sequence of hyperbolic 3–manifolds which have increasing injectivity radius, and which, subject to some conjectures in number theory, are rational homology spheres. We prove unconditionally that these manifolds are rational homology spheres, and give a sufficient condition for a tower of hyperbolic 3–manifolds to have first Betti number 0 at each level. The methods involved are purely pro–p group theoretical.

DOI : 10.2140/gt.2006.10.331
Keywords: pro–$p$ group, hyperbolic 3–manifold, rational homology sphere

Boston, Nigel 1 ; Ellenberg, Jordan S 1

1 Department of Mathematics, University of Wisconsin, Van Vleck Hall, 480 Lincoln Drive, Madison WI 53706, USA 
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Boston, Nigel; Ellenberg, Jordan S. Pro–p groups and towers of rational homology spheres. Geometry & topology, Tome 10 (2006) no. 1, pp. 331-334. doi: 10.2140/gt.2006.10.331

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